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broken link fixed, cf. https://math.meta.stackexchange.com/a/34713/228959
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Glorfindel
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This paperThis paper references an earlier paperearlier paper which suggests (based on very indirect evidence from numerical estimates for the area of the interior) that the boundary may have positive Lebesgue measure. That was the most recent paper I could find on the subject so I tentatively infer that the answer to your question is that to date no-one has managed to calculate the area of the boundary.

This paper references an earlier paper which suggests (based on very indirect evidence from numerical estimates for the area of the interior) that the boundary may have positive Lebesgue measure. That was the most recent paper I could find on the subject so I tentatively infer that the answer to your question is that to date no-one has managed to calculate the area of the boundary.

This paper references an earlier paper which suggests (based on very indirect evidence from numerical estimates for the area of the interior) that the boundary may have positive Lebesgue measure. That was the most recent paper I could find on the subject so I tentatively infer that the answer to your question is that to date no-one has managed to calculate the area of the boundary.

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This paper references an earlier paper which suggests (based on very indirect evidence from numerical estimates for the area of the interior) that the boundary may have positive Lebesgue measure. That was the most recent paper I could find on the subject so I tentatively infer that the answer to your question is that to date no-one has managed to calculate the area of the boundary.